L pLr< •a *s o a* 1 Ph 80 70 60 1 50 40 30 1 20 10 Coal Oil & gas Ind. Min. Groundwater The response of environmental consulting professionals (fig. 2) reflects the high priority given in Kentucky to mitigating pol- luted sites, but it also indicates that the future tasks of prevent- ing pollution and applying geo- logic maps to industrial issues are considered equally impor- tant. Today in year 2000, the U.S. Environmental Protection Agency reports 16 Superfund toxic waste sites in Kentucky on the National Priority List, 132 hazardous waste sites, and 423 toxic release sites in the state. 9 Figure 2 Map use in environmental consulting s/5 a o E it > ■a 'zr> O a. *-> c 8 80 70 60 50 40 30 20 10 Pollution prevention Industrial issues Site cleanup 'Toxic release sites are where toxic chemicals are used, manufactured, treated, transported, and released to the environment. Map use in hazard prevention and protection u V) oCr e o 50- Si 40 u > "t/3 30- ■ o a- 20- c Ui 10- I ■ I p^l Landslides Earthquakes Karst Mine problems subsidence Figure 3 Figure 4 Figure 5 Figure 3 reflects the utility of maps for understanding the causes of geologic hazards, pre- venting their occurrence, and keeping Kentucky's citizens out of harm's way. The number one use of geologic maps for hazard prevention and protection in Kentucky is delineating areas susceptible to karst problems. About 55% of the state is under- lain by karst. Here, dissolution of limestone and dolomite has caused sinkholes, caves, and underground streams. The west-central portion of the state, around Mammoth Cave National Park, is well known for this phenomenon. The three next most significant map uses for hazards are for mine subsidence, landslides, and earth- quakes. Earthquake- related uses will likely increase in western Kentucky as more becomes known about the potential for a major earthquake in the New Madrid region of southeastern Missouri. Figure 4 shows the use of geo- logic maps in maintaining the state's infrastructure and for building, road, pipeline, dam, dike, lock, utility, and railroad construction. Most construc- tion requires high-quality aggregate materials for con- crete, and geologic maps help to locate nearby sources of aggregate, which reduces high transportation costs. Maps also help predict construction and excavation conditions, and help in developing mitigation plans for construc- tion in karst-prone geologic hazard areas. Figure 4 indicates how broad based the application of geology is in the Kentucky economy. c o 8 u > *5 O a. c o o i* •-> 20 18 16 14 12 10 8 6 4 2 Map use in city planning - i i Zoning decisions Landscape planning Building codes Figures 5, 6, and 7 show responses from users of Kentucky's l:24,000-scale geo- logic maps for planning and property valuation. GQ map use for city planning has mainly focused on zoning and landscaping (fig. 5). Population growth and shifting patterns of growth can place considerable stress on an environment if the geo- 8 logic conditions are not compatible with a particular land-use change. Kentucky, like most states, has experienced growth in metropolitan areas. The Natural Resources Inventory for Kentucky shows that urban land grew from 1,238,400 acres in 1982 to 1,955,300 acres in 1997, a 58% increase totaling 1120.2 square miles. The l:24,000-scale geologic quadrangle maps provided planners with answers to critical questions about wise land use. Planners also used geologic maps to help develop building codes. Geologic factors such as earthquakes, subsidence, and karst landscapes have a direct effect on the requirements needed for safe construction. Map use in regional planning Regional planners used geo- logic maps for selecting waste disposal sites, for issuing industrial permits, and, to a lesser extent, for locating transportation corridors (fig. 6). Safe waste-disposal siting cannot be accomplished with- out evaluation of geologic conditions, both regionally and locally. Geologic informa- tion is essential in the permit review process for industrial or other land-use activities that have a potential environmental impact. If geologic maps are not available, information must be obtained from alternative sources, if available, often at a high monetary and time cost. Figure 6 d o a. 8 U > O Cm d % u 1> Cm 50 45 40 35 30 25 20 15 10 5 Site waste disposal Transportation Industrial permits Figure 7 40 Map use in property valuation d o Cm in 4> U 24k 24k 250k 500k 10 The use of computerized and/or digitized products appears to be increasing, as the product-use data in figure 1 1 indicates. Digitized surface photos and scans of conven- tional topographic maps are being used as frequently as dig- ital elevation data files that the user converts to maps. An over- whelming majority (82%) of respondents agreed that digital geologic maps would be valuable to them. Currently, only digitized surface photos, scans of conventional topographic maps, and digital elevation data files are available in digital format at 1:24,000 scale. Conclusions from survey results 1 . Geologic information is fundamental for a large number of economic and environmental applications. 2. Detailed l:24,000-scale GQ maps that include major features — lithology, structural features, and formation contacts — are the need of the future, a need that was correctly anticipated in Kentucky three decades ago. 3. Users consider digital geologic maps to be valuable. Descriptive value judgment As in any study of benefits and costs of a public good, descriptive value judgments are at least as important as quantitative ones to the decision- making process. Often they are more important because they capture intan- gibles and psychological aspects. Users were asked three questions to ascer- tain how GQ maps influence the qualitative aspects of their work. The questions below were aimed at a direct and indirect estimation of user judgement: • Give as many examples as possible of how geologic quadrangle maps improved the quality of your work. • Give as many examples as possible of how geologic quadrangle maps add credibility to your work. • Describe projects in which the lack of geologic quadrangle maps contributed to poor planning or extra cost. We listed the more than 1,300 descriptive answers and separated them into like categories. The following three lists summarize how users see quality and credibility enhanced when maps were used and how they suffered when maps were not available. Figure 11 How geologic quadrangle maps improve quality of work • Users feel more confident in own work • Improved communication among experts (geologists, engineers, planners) • Excellent educational tool for citizens • Provide regional geologic context 11 • Better identification of mineral and groundwater resources • Better mining and quality control decisions • Increased precision in well-drilling (location, depth, success rates) • Improved assessment of groundwater contamination potential • Superior remediation designs in environmental applications • Satisfying regulatory requirements • Aid in court litigation How geologic quadrangle maps add credibility to work • Maps created by pool of scientists without profit motives • They bring standardization of nomenclature • Geological Survey enjoys reputation in business • Aid in verification of own field work • Provide regional context to site-specific geology • Make visualization easy for non-scientists • Regulatory agencies require them for credibility Effects of non- availability of geologic quadrangle maps • Project costs increase by up to 40% • Substantial drop in well-drilling success • Most environmental projects unfeasible without expensive site-by-site mapping by contractor • Cosdy errors in engineering decisions • Delays in project completions • Teaching Kentucky geology difficult The broad economic applications of GQ maps, combined with the improve- ments they enable in quality and credibility of work, make an immeasurable contribution to the state's economy — immeasurable because they are qualita- tive and pervasive throughout the spectrum of economic and environmental activities routinely carried out in Kentucky. Another way to assess the intangible value of GQ maps is to study the nega- tive consequences for projects had the maps been not available. Delays in project completions, diminished success rates, costly mistakes, higher overall expenses, and occasional inability to undertake projects entirely are the conse- quences. The social and political benefits of being able to use GQ maps or the conse- quences of not being able to do so can far exceed the direct monetary conse- quences. An example of both the social and political consequences would be the current discussion about locating waste disposal sites or environmentally sensitive businesses near poorer neighborhoods or neighborhoods with pre- dominantly minority populations. Therefore, the qualitative value of GQ maps discussed above may be far greater than the monetary value discussed in the next section. 12 QUANTITATIVE VALUATION OF GEOLOGICAL QUADRANGLE MAPS Because GQ maps have many different users, emerging and unknown new uses, and repeated uses over time, placing a quantitative valuation on them is an extremely complex problem. Our approach has been to first estimate the value to an individual map user and then to extend that value to all the possible map users over time to get an estimate of the aggregate benefits from the Kentucky geologic mapping program. Theoretical framework Consider a map user who in preparing a project report uses the GQ map to gather technical information about geology and thus makes better decisions. A typical map user could be a consultant using the maps to prepare a report on a project, or other users such as mining companies, county and city planners, construction engineers. The project could be a planned mining and exploration activity, setting up a landfill, or an environmental clean-up operation. Assume that the map user and his or her clients are risk neutral. 10 The map user's objective is to minimize the expected total cost of prepar- ing a given quality project report. Given the information available to the user, he or she chooses the level of effort necessary to prepare the report so that total costs are minimized. Increasing the level of effort will increase the total costs. Let The the level of the consultant's effort, R the credibility of the consultant's report, and a the geologic information available. Then the expected cost function may be represented as £ C^ iU where §>0,f<0,§>0 (1) where EC represents the expected value of the total cost. The specification dC/dT > indicates that each extra unit of effort put in by the consultant increases total costs over the relevant range of the cost function. Similarly, as more geologic information becomes available, the consultant's total costs tend to fall; hence, dC/da < 0. As in the case of effort, the costs increase as the credibility of the report increases, indicated by dC/dR > 0. The consult- ant minimizes his or her expected total cost, choosing the level of effort T, while adhering to a certain minimum level of credibility, i.e., R > R where R is the minimum level of credibility required for the project report. l0 To understand risk neutrality, consider the following numerical example: A choice is given between a) accept $10 for sure or b) roll a dice in a gamble which pays off $100 with a 10% probability and $0 with a 90% probability. The person who prefers a) is risk averse, the per- son who prefers b) is a risk lover, and a person who is indifferent between a) and b) is risk neutral. 13 Mathematically, this problem of the consultant can be represented as Min EC(T, a, R) subject to R > R . (2) The Lagrangian equation for the above minimization problem is L(T, X) = EC(T, a,R) +X(R- R) where X is the Lagrangian multiplier. The Lagrangian multiplier can be interpreted as the value of increasing the credibility of the consultant's report at the margin, say by one unit. In other words, from an economist's perspective, it is the marginal (shadow) value of the credibility of the con- sultant's report. The first-order conditions for the minimization problem defined in equation 2 are dL dC(T, a, R ) , dR(T) JT = —JT + A ~dT = U - (3) dL dX = R(T)- it =0. (4) These first-order conditions define the optimal effort that will minimize the user's cost of preparing the project report. Now consider a scenario when geologic quadrangle maps are not available. In this case, the consultant has only limited prior information about the geologic conditions, attributable to his or her own experience or smaller scale maps. Let cCp depict the prior information. Note that the subscript p refers to the limited prior information because large-scale geologic maps are not available. In most cases such prior information may not be sufficient to complete the task. The consultant will have to put in some extra effort to get additional information so that the credibility constraint R > R is satisfied. The consultant in this situation will have to choose the optimal effort that will minimize the total costs while meeting the credibility standards. Mathematically, the consul- tant's problem under this situation can be depicted as Min EC(T p , a p , R) subject to R > R . (5) where Tis the level of effort put in by the consultant to prepare his or her report when the geologic quadrangle maps are not available. Let T p be the solution to the above minimization problem. Then the expected cost (EC) under optimal effort is £C(7\,, a p , R). Note that the consultant will have to put in some extra effort (in the absence of large-scale geologic maps) to collect the required geologic infor- mation, which will increase the total costs. Intuitively, since the consultant minimizes the costs, he or she will put in only the minimum extra effort required to satisfy the credibility constraint. In other words, the credibility of the report under this scenario will be R. 14 Now consider an alternative scenario when large-scale geologic quadrangle maps are available and the consultant is working on the same problem, but with the maps. Assume that all the relevant geologic information required for the project is available in the maps and that these maps increase the cred- ibility of the report." Let a m represent the geologic information contained in the maps. The subscript m represents the second scenario when geologic maps are available. Note that geologic maps provide much of the relevant information and hence a user prefers a m to a p. When maps are available, the user would not have to put in the extra effort to collect geologic informa- tion required to complete his or her project. The consultant, as in the first scenario, minimizes the expected total costs subject to the standards of cred- ibility. The consultant's problem can then be represented as Min EC(T m) a m R) subject to R > R . (6) Note that the problem defined in equation 6 differs from the one in equa- tion 5. In the latter case the consultant works with the map, while in the former case it is assumed that the consultant works without the map. Let T* m be the solution to the problem defined in equation 6. Then the consul- tant's expected cost is EC(T* m , a m , R). Since T*p > T* m , it follows (by definition, dC/dT > 0) that EC(T* m , a m , R) < EC(T*p, b) = 0, where P is the probability. Thus, a is the respondent's subjective estimate of the lowest possible cost savings from using the map and b is the subjective esti- mate of the highest possible cost savings. In order to obtain subjective esti- mates of a and b, the respondents were asked to reveal their most pessi- mistic and most optimistic estimates, respectively, of the cost savings. They were then asked for their subjective estimate of the most likely cost savings. The most likely value c is the mode of the distribution of V. Once an inter- val [a, b] and the mode c are identified, the next step is to place a probabili- ty density function on [a, b] that is thought to be representative of V. Given the values of a, b, and c, the random variable V is represented by a triangular distribution on the interval [a, b] with mode c (fig. 13). Then the subjective probability density function of Kis (Law and Kelton 1990) ' 2(V-a) if a an< ^ WTP on the average are presented in table 1." The expected minimum value of one quadrangle map to a single user, EV MIN , on the average is $27J76. The expected maximum value of a quadrangle map, EVmax, i s $43,527, and the WTP for the map on the average is $342. It may be noted that these are expected values of one quadrangle map to a single user. A user, however, may use the map for more than one project. Such multiple uses are not accounted for in this study. Hence the estimated values are very conservative. Expected value of the geologic quadrangle maps ($/map/user) EVmin 27,776 EV MAX 43,527 WTP 342 Table 1 The expected minimum value of the map, EV MIN , ranged from $43 to $396,800 (appendix 2). The expected maximum value, EV MAX , ranged from $13 to 396,800 (appendix 3). The expected values of WTP ranged from about $4 to $3,340 (appendix 4). Aggregation of benefits, mapping costs, and determination of socially optimal level of investment in mapping programs Theoretical basis for benefit aggregation As for most public goods, markets do not exist for GQ maps in the sense that they exist for private goods such as cars or computers. Each individual user probably derives different marginal benefit from the maps. 13 Consider figure 14, in which the horizontal axis L represents the scale of GQ maps and the vertical axis represents their marginal value to the user. The cost of mapping increases with scale, while the marginal increase in benefits of larger 'The parameters of the probability distribution of V um , V MAX and WTP and the expected values for the individual respondents are presented in appendixes 2, 3, and 4. The incom- plete answers to questions 14b, 14c, and 14d are summarized in appendixes 5-11. "Our results show that valuations are different for different users, see appendixes 2, 3, and 4. 19 Aggregation of map values over n users Figure 14.3 V _ _>^Di Figure 14.1 XI L V \d 2 Figure 14.2 ^2 " " " iV scale maps declines. 14 The curve D^ in figure 14.1 represents the marginal benefits derived by individual 1. Similarly the curve X>2 in figure 14.2 represents the marginal benefits derived by indi- vidual 2. The curve MC in figure 14.3 is the marginal cost of producing the maps of increasing scales. If we suppose that there are n map users i = ( 1, . . ., n), the aggregate marginal benefit is obtained from a vertical aggregation of the individual benefit curves, as in figure 14.3. The socially optimal scale of maps, then, is obtained by equating the marginal cost of producing the maps to the marginal social benefits derived from their use. In figure 14.3, the aggregate marginal social benefit V is equal to the marginal costs when the map scale is L. Thus, if the scale L is chosen (along with the cost that it implies), the marginal bene- fit derived by individual 1 is Vj as in figure 14.1 and by individ- ual 2 is V 2 2S in figure 14.2. Because the cost of mapping increases with scale, L can serve as proxy for the investment in mapping programs. To generalize, when the generation of maps is at the socially optimal level L, the marginal benefits derived by each individual user is V;. The total social benefits are represent- ed then by the area ABLO, and the area ABC represents the net social ben- efits. The marginal benefits and costs associated with different scale maps were not solicited from map users in this study, and, thus, the estimation of the areas ABLO and ABC was not targeted. The benefits also accrue over a 20 14 The assumption of declining marginal benefits with increasing map scale is based on the rationale that the highest benefits are derived from even the smallest scale geologic maps when no geologic maps exist at all. From this point on, as geologic maps of larger scale become available their additional value is successively smaller than that of the very first (smallest scale) geologic map ever made available. There will be exceptions to this rule, for example, when a larger scale map may be absolutely essential for a specific application or where a smaller scale map will not do. However, the general rule of diminishing marginal value remains valid as map scale increases. period of time into the future as new uses may arise in the future. Such future benefits were also not included in this study. A discrete estimate of the aggregate value of GQ maps at 1:24,000 scale is obtained as I Vi i = l where n is the number of map users. These estimates of the average expect- ed values of GQ maps to the individual map users are listed in table 1. The aggregate yearly benefits are estimated by multiplying the number of users by the average value of map to an individual user. The number of map sales is used as a proxy for the number of map users. We assume that each indi- vidual buyer will use the map for at least one project and may use the map for more than one project. The results based on the above assumption thus provide a conservative estimate of the aggregate benefits. A second dimension in the estimation of aggregate benefits is aggregation over time. We have estimated the value of the maps on the basis of data collected in 1999. We recognize that estimates of value expressed in 1999 may or may not reflect the values in the past years because of evolving markets and legal and technological environments. However, the scope and costs of projects for which maps were used also evolved over time. The rel- ative value of GQ maps to the user in the contexts of past projects can, therefore, be assumed to be similar to their current assessment. Thus, the 1999 estimates of value were multiplied by the numbers of GQ maps sold in the past years to arrive at their aggregate value over time. Empirical estimate of aggregate benefits Kentucky geologic maps were produced by the U.S. Geological Survey but were sold by USGS, KGS, and the Kentucky Department of Commerce (KDC). Sales records available are primarily limited to those of KGS. Even these are limited to the 1972-1977 (Cressman and Noger 1981) and 1995-1999 15 periods. Accordingly, the number of maps sold by KGS in these 11 years alone totaled about 65,000. At least 16,000 more maps were sold by KDC in the three-year period of 1974-1976 (Cressman and Noger 1981). No records for the remaining years of sales by KGS and KDC are available, nor are the sales records by USGS for any of the years since the start of the program. The documented sales of Kentucky geologic maps total about 81,000. It is conceivable that at least three times as many more maps were sold in other years for which no data are available. Without speculating about the actual map sales, we base the following calculations on a (conservatively low) total sales volume of 81,000 GQ maps. * The expected minimum aggregate value of GQ maps then would be 81,000 x $27,776 = $2.25 billion in 1999 dollars. * The expected maximum aggregate value of GQ maps would be 81,000 x $43,527 = $3.53 billion in 1999 dollars. 'Personal communication from Bart Davidson, Kentucky Geological Survey. ~ , The aggregate willingness to pay (WTP) for the GQ maps would be 81,000 x $342 = $27.7 million in 1999 dollars. The total mapping expenses for the State of Kentucky mapping program completed in the 1961 to 1978 period were estimated to be $16,035 mil- lion in 1960 dollars (Cressman and Noger 1981) or $90 million in 1999 dollars, based on the Consumer Price Index. The above results aggregated over time indicate that, in monetary terms, the estimated total value of the mapping program at the minimum is at least 25 times the cost of the pro- gram. The estimated maximum aggregate value of the Kentucky mapping program is 39 times the cost of the program. In other words, the minimum net social surplus from the mapping program is $2.16 billion in 1999 dol- lars. Although the aggregate WTP is estimated to be about 31% of the cost of the program, it must be remembered that the value estimates are based on only 1 1 years of map sales data from KGS and 3 years of sales data from KDC and ignore all sales by USGS. Another way to compare these estimated values to the cost of GQ mapping is to consider the average payback period in terms of the number of proj- ects in which a quadrangle map is used. The cost of mapping the 707 quadrangles in Kentucky totaled about $90 million in 1999 dollars, or $127,300 per quadrangle. With an average EV MIN value of $27,776 per quadrangle map per project, the mapping project for an individual quadran- gle breaks even when a quadrangle map is used in about 5 projects. If we consider the EVj^j^x value of $43,527, the cost of mapping one quadrangle is paid back when the map is used in about 3 projects. The most conserva- tive estimate of the total number of maps sold is around 81,000 or an aver- age of about 114 maps of each quadrangle. It may also be noted that a buyer may use the same map for multiple projects over a period of time. Whether the break-even point is reached after 3 or 5 project uses, it is evi- dent that the average sales per quadrangle of 1 14 maps are indicative of benefits exceeding costs by ratios of about 23:1 and 38:1, which are close to those calculated previously. A third way of looking at the results is to compare the average estimated dollar values with the estimates of the proportions of project costs the geo- logic information accounts for as represented in figure 13. The average expected minimum value of $27,776 per quadrangle map is plausible when we consider that, on the average, about 17% of project cost is attributable to obtaining geologic information when maps are not available. 16 This per- centage would put the average total project cost (size) at about $164,000. Considering the same share of 17% and the average expected maximum value of a GQ map of $43,527, the total project cost (size) would be about $256,000. Based on our experience with GQ map users, geologists, and project managers, we think that these numbers are plausible. This context lends credibility to the expected minimum and maximum values deter- mined from the responses. 22 '"The share of total project cost that would be spent on obtaining geologic information when maps are not available (question 9, appendix 1) on the average was 17%. Even using these very conservative sales figures, this is a surprisingly robust value for a public good. Since GQ maps are a non-excludable public good, the full benefits of the maps accrue to any individual user even if that indi- vidual willingly pays only a negligible price (the "free rider syndrome"). User response to question 14B in the questionnaire confirms that users are not willing to pay the full cost of producing the map. Yet, based on only a fraction of the map sales data, users have shown the willingness to pay at least 31% of the cost of the mapping program in Kentucky. The actual number of maps sold until now is estimated to be at least two to three times higher, indicating that users are probably willing to pay fully for the cost of the mapping program in Kentucky. Considering the additional intangible benefits of geologic maps described in the first part of the report, we conclude that the geologic mapping program in Kentucky has been an excellent public sector investment for society. The above results are based on the assumption of zero real discount rates. An alternative scenario could be to assume a real discount rate of 1 or 2% above inflation. In our basic calculations, we have adjusted the cost of the mapping program for inflation by using the Consumer Price Index (CPI) instead of discounting the benefits to a past date; i.e., we have assumed a zero real discount rate above inflation. Assuming that the mapping costs increased by 1% above inflation annually (1% real discount rate), the cost of the mapping program in 1999 dollars would be $130 million. In this case, the minimum expected value of the GQ maps would be 17 times the cost, the maximum expected value would be 27 times the cost, and the WTP would be 0.21 times the cost. Alternatively, if the cost of the mapping pro- gram were increased by 2% above inflation annually (2% real discount rate), it would be $188 million in 1999 dollars, and the ratios would be about 12:1 for the minimum expected value, 18.5:1 for the maximum expected value, and 0.15 for the WTP. Note that these very conservative scenarios, also based on only a fraction of the map sales data, indicate that investment in geologic mapping has been highly productive and that the returns to mapping investment far exceeded the costs. SUMMARY AND CONCLUSIONS This study was conducted in Kentucky because it is the only state that has completed l:24,000-scale geologic mapping, published maps for all quad- rangles, and seen at least two decades of map use. Sufficient time has elapsed to evaluate which sectors of Kentucky's economy have been using GQ maps, the reasons for using the maps, and how much the maps have been worth to the users. Studies of the value of public investments are difficult because of their intan- gible and future benefits. This empirical study is anchored in solid founda- tions of economic theory of public goods and uses the most conservative assumptions possible. A total of 2,200 actual and potential users of geologic maps was polled. The response rate of 20% (440 responses) provides a representative sample of the 23 user population. It includes geologists working independently or for mining or utility companies, geology teachers, county and city planners, and govern- ment employees involved in environmental and other regulations concerning health and safety. While it is impossible to identify the whole user popula- tion, we believe that a very large fraction of the user population has been polled and given an opportunity to participate. Users were asked to answer a questionnaire designed to solicit data on map uses, desirable map features, and subjective dollar value of maps to the users. Map use The user responses indicate that GQ maps are used in nearly all sectors of the economy to ensure environmental safety, to prevent hazards to man- made structures, and to explore and develop natural resources such as groundwater, minerals, and fuels. The use of GQ maps improves the quality and credibility of work and saves money. Most importantly, geologic map- ping generates knowledge, a public good vital to the economy, public safe- ty, and public health. This knowledge would not be produced if left to pri- vate enterprise, and has not been produced by private enterprise elsewhere, except on a site-specific basis or under contract to a public agency. Map users indicated the desirability of lithology, structural features, formation contacts, and cultural features in maps. The most desirable map scale was 1:24,000. Although most users currently use maps as overlays, copies, enlargements, and in AutoCAD and GIS, they indicated an overwhelming desire for digital maps for the future. Map value The aggregate value of GQ maps in this study was based on only a fraction of actual sales data. On the basis of the user response, the study computed the average minimum and maximum expected values of a quadrangle map to be $27,776 and $43,527 We calculated the aggregated value of GQ maps sold over a fraction of the study years to be at least $2.25 billion at the minimum and $3.53 billion at the maximum in 1999 dollars. The cost of the geologic mapping program in Kentucky was about $90 million in 1999 dollars. The value of the geologic maps to the users was at least 25 to 38 times higher than the cost of the mapping program. When cost esti- mates for the mapping program were inflated by 1% per year above infla- tion, the value of the maps outweighed costs by a minimum margin of 17:1 and a maximum of 28:1. Even when mapping costs were inflated by 2% per year above the rate of inflation, the value remained comfortably higher than costs, at a minimum ratio of 12:1 and a maximum of 18.5:1. The average willingness to pay (WTP) was reported to be $342 per map. The very limited map sales data available indicate a WTP/mapping cost ratio of 0.31. Complete map sales data would raise the ratio to cover the entire cost of the mapping program and probably much more. Case studies of public policy decisions and projects involving public goods indicate that WTP/cost ratios less than one are not uncommon. Since public goods are non-excludable, individual users may not be willing to pay the full cost of 24 providing the public good as he or she will not get exclusive rights to the good. He or she pays only a user fee that is much less than the cost of pro- ducing and facilitating the public good. Hence a WTI/cost ratio less than one is not an unexpected result. Finally, a whole section of this study is devoted to intangible benefits derived by map users. 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Berg, R. C, N. K. Bleuer, B. E. Jones, K. A. Kincare, R R. Pavey, and B. D. Stone, 1999, Mapping the Glacial Geology of the Central Great Lakes Region in Three Dimensions — A Model for State-federal Cooperation: U. S. Geological Survey Open-File Report 99-349, 64 p. Bernknopf, R. A., D. S. Brookshire, D. R. Soller, M. J. McKee, J. F. Sutter, J. C. Matti, and R. H. Campbell, 1993, Societal Value of Geologic Maps: U. S. Geological Survey Circular 1111, 53 p. Bessler, D. A., 1981, Some Theoretical Considerations on the Elicitation of Subjective Probability: Department of Agricultural Economics, Purdue University, West Lafayette, Indiana, Bulletin No. 332. Bhagwat, S. B., and R C. Berg, 1991, Benefits and Costs of Geologic Mapping Programs in Illinois — Case Study of Boone and Winnebago Counties and Its Statewide Applicability: Illinois State Geological Survey Circular 549, 40 p. Bohm, P., 1991, An approach to the problem of estimating demand for public goods: Swedish Journal of Economics, v. 73, p. 94-105. Brent, R. J., 1996, Applied Cost-Benefit Analysis: Edward Elgar Publishing Company, Northampton, Massachusetts, v. 74. p. 336. Brookshire, D. S., B. C. Ives, and W. D. Schultze, 1976, The valuation of aesthetic preferences: Journal of Environmental Economics and Management, v. 3: p. 325-346. Cressman, E. R., and M. C. Noger, 1981, Geologic Mapping of Kentucky — A History and Evaluation of the Kentucky Geological Survey-U. S. Geological Survey Mapping Program, 1920-1978: U. S. Geological Survey Circular 801, 22 p. Gould, J. P., 1974, Risk, stochastic preference, and the value of information: Journal of Economic Theory, v. 8, p. 64-84. Hanley, N., and O. L. Spash, 1993, Cost-Benefit Analysis and the Environment: Edward Elgar Publishing Company, Northampton, Massachusetts, 278 p. Hess, J., 1980, Risk and gain from information: Journal of Economic Theory, v. 27,231-238. Laffont, J. J., 1989, The Economics of Uncertainty and Information: The MIT Press, Cambridge, Massachusetts, 289 p. Law, A. M., and W. D. Kelton, 1990, Simulation Modeling and Analysis. McGraw-Hill Book Company, New York. McGrain, P., 1966, Some Economic Aspects of Kentucky's Geologic Mapping Program: Society of Mining Engineers, preprint 66H301, 10 p. McGrain, P., 1967, The Application of New Geologic Maps to the Economic Growth of Kentucky: Kentucky Geological Survey, Series 10, Special Publication 14. McGrain, P., 1979, An Economic Evaluation of the Kentucky Geologic Mapping Program: Kentucky Geological Survey, Series XI, 12 p. 26 Randall, A., B. C. Ives, and C. Eastman, 1974, Bidding games for evaluation of aesthetic environmental improvement: Journal of Environmental Economics and Management, v. 3, p. 325-346. Samuelson, P. A., 1954, The pure theory of public expenditure: The Review of Economics and Statistics, v. 36, p. 387-389. U. S. Geological Survey, 1999a, Sustainable Growth in America's Heardand — 3-D Geological Maps as the Foundation: U.S. Geological Survey Circular 1190, 17 p. U. S. Geological Survey, 1999b, The Quality of Our Nation's Waters, Nutrients and Pesticides: U.S. Geological Survey Circular 1225, 82 p. Young, D. L., 1983, A Practical Procedure for Eliciting Subjective Distributions, Paper presented at the American Economics Association meeting, West Lafayette, Indiana. Related readings Illinois State Geological Survey, 1996, Break from Tradition, Annual Report, 26 p. Illinois State Geological Survey, 1997, New Directions, Annual Report, 30 p. Illinois State Geological Survey, 1998, Geology for a New Generation, Annual Report, 58 p. Just, R. E., D. L. Hueth, and A. Schmitz, 1982, Applied Welfare Economics and Public Policy: Prentice Hall, Inc., New Jersey. Marchak, J. and K. Miysawa, 1968, Economic comparability of information sys- tems: International Economic Review, v. 9, p. 137-141. Preckel, P. V., E. T. Loehman, and M. S. Kaylen, 1987, The value of public infor- mation for microeconomic production decisions: Western Journal of Agricultural Economics, v. 12, p. 193-197. Roe, T, and F. Antonovitz, 1985, A producer's willingness to pay for information under price uncertainty: Theory and application: Southern Journal of Economics, v. 52, p. 382-391. Sugden, R., and A. Williams, 1978, The Principles of Practical Cost-Benefit Analysis: Oxford University Press, New York, NY. 275 p. U.S. Environmental Protection Agency, 2000, Envirofacts Warehouse, [ www.epa.gov/superfund/sites/index.htm1 and [www.epa.gov/opptintr/ tri/tri97/pdf/97state/kv97.pdn . 27 Appendix 1 Questionnaire: Assessment of benefits of geologic quadrangle maps of Kentucky 1. Activities in your organization that may require the use of geologic quadrangle maps: (Check all that apply) Exploration and development □ Coal □ Groundwater □ Oil and natural gas □ Other (specify) □ Industrial minerals (limestone, sand/gravel, clay, ore deposits) Environmental consulting D Pollution prevention □ Site cleanups □ Industrial Hazard prevention/protection □ Land slides □ Karst problems □ Earthquakes □ Subsidence Engineering applications □ Buildings and foundation problems □ Pipelines, □ Roads/highways □ Utilities, □ Railroads LI Dams, dikes, river locks City planning □ Zoning decisions □ Building codes □ Landscape design and planning Regional planning □ Siting waste disposal facilities □ Permitting industrial facilities □ Transportation Property valuation □ For tax purposes □ Land acquisitions 2. What percentage of your work in the last five years depended on using geologic quadrangle maps? □ By number of projects (%) □ By hours (%), □ By dollar value (%) 3. What features shown on the geologic quadrangle maps are important for your work? □ Lithology □ Formation contact □ Structural features □ Relationship of the above to cultural features What features would you want on geologic quadrangle maps that are currently not on such map? Please list: 4. How do you use geologic quadrangle maps: □ Overlay with other data □ Put into Auto CAD or GIS, then manipulate □ Photocopy, reduce or enlarge for technical reports 5. What scale of geologic maps is most useful to you? □ Larger than 1:24,000 □ 1:250,000 □ 1:24,000 □ 1:500,000 28 6. Which, if any, of the following digital map products are you using now? (Check all that apply.) □ Digital Orthophoto Quarter Quads (DOQQs) D Digital Elevation Model (DEMs) □ Digital Roster Graphic (DRGs) Other (specify) 7. Would digital geologic maps be of value to you? □ Yes □ No Comments: 8. How do you obtain the needed information if there is no geologic quadrangle map? □ Own field work □ Hire a consultant □ Contract Geological Survey 9. On a typical project for which there is no geologic map, what percentage of total project cost would be spent on obtaining geologic information? %. 10. Give as many examples as possible of how geologic quadrangle maps improved the quality of your work. (Use separate sheet if necessary.) 1 1 . Give examples of how geologic quadrangle maps add credibility to your work. (Use separate sheet if necessary.) 12. Describe projects in which the lack of geologic quadrangle maps contributed to poor planning or extra cost? Explain how. (Use separate sheet if necessary.) 13. Estimate the dollar value of geologic quadrangle maps in Kentucky for you or your company. $ . Please explain. 14. Case example: A. Name a particular project for which you used geologic quadrangle maps. B. Had the maps not been available, how much money would you have willingly spent to get the information contained in the maps for the above use? (We know that this and the following questions are difficult but give us the best estimate.) □ Maximum spent $ D Minimum spent $ □ Best estimate of money spent $ C. Estimate the money you saved because of the availability of maps. □ Maximum savings $ □ Minimum savings $ □ Best estimate of savings $ D. Given the value of the map to you, how much money would you have paid for the map? □ Maximum $ □ Minimum $ □ Actual payment $ If you wish to identify yourself and your company by name, please do so here. SBB/isgs/June23,1999 Appendix 2 Parameters of the distribution of the minimum value of the map ( V MIN ) and expected values (EV MIN ; $) ID# a b c ^v min ID# a b c by min 2 40,000 75,000 50,000 54,560 227 50 250 100 132 5 5,000 10,000 250,000 87,627 239 10,000 20,000 12,000 13,888 9 2,000 5,000 5,000 3,968 244 30,000 60,000 50,000 46,293 10 3,000 100,000 50,000 50,592 245 1,000 5,000 2,000 2,645 12 3,000 15,000 12,000 9,920 251 1,000 10,000 3,000 4,629 17 100 1,000 50 380 264 2,000 10,000 50 3,985 30 4,000 10,000 7,000 6,944 267 150 300 75 174 51 2,000 10,000 4,000 5,291 268 250,000 500,000 65,000 269,493 52 800 1,400 900 1,025 276 6,500 12,500 8,000 8,928 54 2,000 4,000 2,000 2,645 278 1,000 5,000 2,000 2,645 59 2,000 10,000 3,000 4,960 293 10,000 25,000 30 11,583 63 40,000 75,000 50,000 54,560 324 5 500 100 200 83 5,000 30,000 5,000 13,227 330 1,000 10,000 1,000 3,968 88 500 1,000 100 529 336 15,000 50,000 3,000 22,485 91 100 550 1,000 546 339 10 200 10 73 93 10,000 50,000 20,000 26,453 340 500 2,500 2,000 1,653 96 100 250 125 157 343 200 500 300 331 119 25 250 75 116 346 500 5,000 1,500 2,315 136 100,000 250,000 150,000 165,333 347 5,000 10,000 8,000 7,605 146 15,000 25,000 525,000 186,827 348 500 7,000 2,000 3,141 149 5,000 100,000 25,000 42,987 351 1,000 5,000 2,500 2,811 152 500 2,000 1,000 1,157 354 300 2,000 500 926 160 100 500 500 364 375 1,000 50,000 25,000 25,131 162 2,000 150,000 80,000 76,715 378 20,000 50,000 40,000 36,373 163 10,000 25,000 18,000 17,525 386 500 1,500 1,500 1,157 164 1,000 10,000 100 3,670 392 ' 1,500 5,000 500 2,315 169 4 500 100 200 393 500 1,000 50 513 176 50 150 100 99 394 250,000 500,000 450,000 396,800 186 10,000 20,000 10 9,923 398 10,000 50,000 25,000 28,107 190 5,000 20,000 15,000 13,227 399 10 100 20 43 199 1,000 2,000 1,980 1,647 411 10,000 25,000 15,000 16,533 201 500 2,000 1,000 1,157 422 200 5,000 350 1,835 205 500 1,000 500 661 434 100,000 200,000 150,000 148,800 216 1,000 1,500 500 992 436 100 500 150 248 224 1,000 5,000 2,500 2,811 Mean V mN 27,776 Max V MlN 43 Min V MIN 396,800 30 Appendix 3 Parameters of the map of the distribution of the maximum value ( v max) and expected values (EVmaj6 $) ID# a b c EV MAX ID# a b c EV MAX 2 300,000 500,000 400,000 396,800 224 1,000 15,000 1,200 5,687 5 5,000 10,000 250,000 87,627 244 10,000 25,000 10,000 14,880 9 5,000 10,000 10,000 8,267 245 500 1,000 700 727 10 10,000 90,000 90,000 62,827 264 5,000 9,000 7,000 6,944 50 5,000 15,000 10,000 9,920 267 50 200 100 116 51 2,000 10,000 4,000 5,291 268 185,000 435,000 245,000 286,027 52 700 1,300 800 926 276 1,250 2,500 1,500 1,736 54 40,000 50,000 40,000 42,987 278 500 2,000 1,000 1,157 59 2,000 10,000 3,000 4,960 293 10,000 25,000 24,000 19,509 63 300,000 500,000 400,000 396,800 330 1,000 10,000 10,000 6,944 83 10 20 10 13 336 10,000 20,000 15,000 14,880 88 100 900 900 628 346 500 5,000 1,500 2,315 93 8,000 45,000 18,000 23,477 348 300 5,000 1,500 2,249 96 250 1,000 500 579 351 500 4,000 2,500 2,315 119 25 $250 75 116 354 300 1,700 200 727 136 100,000 250,000 150,000 165,333 355 100 15,000 3,000 5,985 146 10,000 20,000 50,000 26,453 375 1,000 50,000 25,000 25,131 152 500 2,000 1,000 1,157 378 20,000 50,000 40,000 36,373 164 10,000 100,000 1,000 36,704 379 25,000 50,000 40,000 38,027 170 3,000 10,000 5,000 5,952 386 500 1,500 1,500 1,157 176 50 150 100 99 392 1,000 4,500 2,500 2,645 190 20,000 60,000 40,000 39,680 393 450 850 700 661 199 30,000 40,000 40,000 36,373 394 250,00C 500,000 450,000 396,800 201 500 1,000 1,000 827 398 10,000 50,000 25,000 28,107 205 1,000 10,000 5,000 5,291 422 25 4,500 500 1,662 216 1,000 1,500 1,500 1,323 436 100 500 150 248 Mean V MAX 43,527 Min ''max 13 Max ''max 396,800 »R>r> ***v MN 9 2001 31 Appendix 4 Parameters of the distribution of the willingness to pay for the map (WTP) and expected values (EV^rm $) ID# a b c EVun, ID# a b c •C V\\TP 9 500 1,000 10 499 197 18 200 18 78 10 5,000 5,000 100 3,340 199 250 500 20 255 12 5 100 4 36 201 8 20 8 12 17 4 10 4 6 216 50 250 150 149 30 10 100 15 41 224 2 1,000 5 333 50 5 30 10 15 227 4 4 4 4 52 5 75 15 31 244 200 2,000 500 893 59 5 20 5 10 245 50 200 100 116 77 7 25 7 13 251 6 100 6 37 91 15 100 15 43 268 8 12 8 9 96 5 10 7 7 276 125 250 150 174 117 10 25 12 16 278 15 30 15 20 118 2 25 5 11 293 10 15 8 11 119 5 10 8 8 320 5 10 3 6 146 100 1,000 500 529 341 5 10 5 7 149 75 5,000 125 1,719 348 100 500 100 231 152 5 25 5 12 351 10 15 2 9 160 25 50 50 41 354 300 750 350 463 164 50 100 10 53 361 5 10 5 7 170 3 12 4 6 386 15 50 20 28 176 5 20 10 12 392 50 5,000 50 1,686 186 50 100 10 53 398 1,000 5,000 4 1,985 188 500 1,000 50 513 399 5 50 10 21 190 500 2,000 1,200 1,223 422 5 20 12 12 Mean WTP 342.19 Min WTP 3.97 Max WTP 3,339.73 32 Appendix 5 Parameters of the distribution of the minimum value of the map V MIN ($) in cases where information provided is incomplete Responder ts who provided a and b only Respondents who provided b and c on ID# a b ID# b c 77 500 2,500 11 3,000 3,500 89 5,000 10,000 15 2,500 350 124 10 75 117 1,000 300 143 10,000 100,000 122 200 10 153 50 1,000 126 100,000 5,000 154 3,000 6,000 197 200 100 156 500 5,000 247 100,000 50,000 178 100 500 260 5,000 50 179 25 75 284 5,000 500 188 2,000 10,000 286 1,000 100 219 7 100 350 10,000 2,500 225 10,000 50,000 365 35 35 237 25 1,000 367 10,000 500 241 5 10 417 100 25 254 500 2,000 275 15,0000 600,000 Mean V MIN 17,003 4,498 289 2,000 10,000 M.mV MIN 35 10 313 25 75 MaxFj,™ 100,000 50,000 341 500 2,000 342 300 1,500 Respondents who provided a only 349 100 30 200 3,000 ID# a 355 214 100,000 366 500? 25? 261 1,000 372 1,000 200,000 383 20,000 374 300 500 387 25,000 397 1,000 5,000 400 500 1,800 Mean V MIN 36,500 402 500 5,000 MinF; w/N 1,000 424 1,000 4,000 MzxV MIN 100,000 Mean V MlN 6,749 36,476 Min V MIN 5 10 Max V MIN 15,000 600,000 33 Appendix 6 Parameters of the distribution of the niinirnuni value of the map (V MIN ; $) in cases where information provided is incomplete Respondents who provided b only Respondents who provided c only ID# b ID # c 4 500 26 300 14 500 42 200 18 1,000 48 10,000 19 2,000 76 800 43 500 84 80,000 46 200 95 2,000 50 10,000 118 500 53 500 138 250,000 72 25,000 140 5,000 81 60,000 145 5,000 82 1,000 151 1,000 94 50,000 157 80,000 142 10,000 159 10,000 155 200 183 100,000 161 500 184 2,000 171 1,800 192 5,000 182 50,000 193 500 206 1,000 210 10,000 223 200 211 10,000 230 10,000 236 50,000 248 100 249 250 273 1,000 257 400 281 10,000 266 500 298 500 280 200 306 10,000 288 15,000 307 8,000 344 4,000 314 1,000 359 5,000 317 1,000 362 20,000 320 1,000 369 10,000 325 10,000 395 5,000 356 30,000 406 25,000 361 10,000 410 1,000 376 50 415 200 404 1,000 416 4,000 408 200 421 3,000 426 1,000 423 5,000 437 10,000 429 10,000 430 500 435 4,000 Mean b 8,642 Mean c 18,855 Min b 50 Min c 200 Max b 60,000 Max c 250,000 34 Appendix 7 Parameters of the distribution of the maximum value of the map i^MAXy $) m cases where information provided is incomplete Respondents who provided b only Respondents who provided c only ID# b ID# c 14 500 18 500,000 43 1,000 26 500 46 200 42 100 53 2,000 72 100,000 82 1,000 76 800 94 1000,000 84 80,000 142 10,000 95 15,000 147 2,000 118 1000 154 6,000 124 50 178 5,000 126 10,000,000 182 100,000 129 500 186 1,000 138 250,000 219 100 140 4,000 227 150 145 5,000 241 1,000 151 600 243 50,000 159 10,000 248 90 161 350 254 20,000 169 1,000 281 9,800 171 24,000 284 4,500 179 25 286 10,000 183 100,000 301 250 184 1,000 306 20,000 192 5,000 307 5,000 193 500 314 1,000 206 500 320 100,000 210 8,000 322 300 211 50,000 325 5,000 218 10,000 342 5,000 236 24,000 356 30,000 249 400 362 200 257 350 366 15,000 260 4,950 367 9,000 266 500 376 35 273 100,000 395 2,000 280 200 404 500 288 10,000 426 1,000 344 40,000 359 5,000 Mean b 3,8341 361 100,000 Min b 35 370 2,000 Max b 1,000,000 372 100,000 374 100 387 18,000 397 3,000 408 500 410 1,000 416 20,000 421 10,000 423 5,000 429 10,000 430 400 Mean c 227,908 Min c 25 Max c 10,000,000 35 Appendix 8 Parameters of the distribution of the minimum value of the map ( V MIN ; $) 36 Respondents who provided b and c only Respondents who provided a and b only ID# b c ID# a b 11 250,000 250,000 4 100 2,500 12 2,000 5,000 77 500 2,500 91 1,000 1,000 89 5,000 8,000 117 1,000 300 143 25,000 175,000 122 190 190 188 2,000 10,000 149 95 10,000 225 10,000 50,000 162 100,000 10,000 237 100 5,000 163 20,000 15,000 251 10,000 1,000,000 197 40 40 261 1,000 1,000 247 100,000 50,000 313 25 60 289 25,000 20,000 349 500 5,000 340 10,000 50,000 406 20,000 40,000 347 1,000 800 411 5,000 10,000 350 10,000 2,500 365 30 30 Mean V Mm 6,094 100,697 399 100 100 Min V MiH 25 60 MaxV Mm 25,000 1,000,000 Mean V Ml , 32,528 25,935 Min V Mm 30 30 Max V Mi „ 250,000 250,000 Respondents who provided a only ID# a 48 100,000 214 100,000 324 500 383 15,000 405 50,000 424 100,000 435 1,000 437 10,000 Mean V Mm 47,063 MinF tfm 500 Max7 iV/ „, 100,000 Appendix 9 Parameters of the distribution of the maximum value of the map (Vmax> $) m cases where information provided is incomplete Respondents who provided b only Respondents who provided c only ID# b ID# c 14 500 18 500,000 43 1,000 26 500 46 200 42 100 53 2,000 72 100,000 82 1,000 76 800 94 1,000,000 84 80,000 142 10,000 95 15,000 147 2,000 118 1,000 154 6,000 124 50 178 5,000 126 10,000,000 182 100,000 129 500 186 1,000 138 250,000 219 100 140 4,000 227 150 145 5,000 241 1,000 151 600 243 50,000 159 10,000 248 90 161 350 254 20,000 169 1,000 281 9,800 171 24,000 284 4,500 179 25 286 10,000 183 100,000 301 250 184 1,000 306 20,000 192 5,000 307 5,000 193 500 314 1,000 206 500 320 100,000 210 8,000 322 300 211 50,000 325 5,000 218 10,000 342 5,000 236 24,000 356 30,000 249 400 362 200 257 350 366 15,000 260 4,950 367 9,000 266 500 376 35 273 100,000 395 2,000 280 200 404 500 288 10,000 426 1,000 344 40,000 359 5,000 Mean b 38,341 361 100,000 Min b 35 370 2,000 Max b 1,000,000 372 100,000 374 100 387 18,000 397 3,000 408 500 410 1,000 416 20,000 421 10,000 423 5,000 429 10,000 430 400 Mean c 227,908 Min c 25 Max c 10,000,000 37 Appendix 10 Parameters of the distribution of willingness to pay ( WTP) for the pay in cases where information provided is mcomplete Respondents who gave c only Respondents who gave &and c ID# c ID# b c 11 2 15 25 4 76 800 21 50 4 126 5 48 1,000 25 140 2,000 51 200 25 151 8 54 10 5 159 10,000 72 25 4 183 100,000 83 100 4 266 5 122 200 10 280 15 136 15,000 15 324 5 147 20 4 387 2 161 15 6 393 5 162 30 10 397 50 179 25 6 406 25,000 218 15 4 435 4,000 257 400 4 260 20 3 Mean WTP 9,460 264 200 10 Min WTP 2 297 100 4 Max WTP 100,000 330 500 10 340 25 25 347 25 10 Respondents who provided a and b 362 100 7 ID# a b 365 375 30 10 4 45 100 300 5 92 2 5 400 25 6 171 250 533 408 10 5 205 5 20 417 50 10 225 50 100 237 10 100 Mean WTP 674 8 241 5 10 Min WTP 10 3 261 1,500 1,000 Max WTP 15,000 25 313 2 20 346 5 25 350 500 10,000 Respondents who provided a only 355 3 500 150 ID# a 366 25 145 100 372 25 1,000 169 4 394 15 30 236 20 411 2,000 8,000 416 10 436 5 25 Mean WTP 34 Mean WTP 265 1,283 Min WTP 4 Min WTP 2 5 Max WTP 100 38 Appendix 11 Parameters of the distribution of willingness to pay (WTP) for the map in cases where information provided is incomplete Respondents who provided b only ID# b 4 500 14 100 18 1,000 28 8 42 8 43 25 46 200 53 500 82 10 85 5 93 15 124 75 142 500 154 100 178 1,000 182 10 210 100 212 10 230 10,000 243 20 249 20 273 1,000 281 500 284 100 286 5 288 100 289 25,000 301 100 302 2,000 306 100 314 4 322 50 344 50 346 25 356 25 359 1,000 367 100 374 500 376 25 395 2,000 404 200 405 500 409 10 415 20 421 25 426 2,000 430 500 437 50 Mean b 1,046 Min b 4 Max b 25,000 39